Some examples of research conducted in this project: Researchers often collect multivariate binary response data to compare naturally ordered experimental conditions. Some examples of ordered experimental conditions include doses in a dose-response study, cancer stages in clinical oncology, and time points in a time-course experiment. For example, the National Toxicology Program routinely conducts dose response studies to evaluate toxicity and carcinogenicity of chemicals. Typically, for each organ within each animal in the study, they record the presence and absence of tumor. Thus on each animal they obtain multivariate binary response vector where some of the components are potentially dependent. For example, mammary gland and pituitary gland tumors are known to be correlated. In such situations statistical methods that ignore the underlying dependence structure, and analyze one binary response at a time, can potentially be underpowered. In this research program we are developing multivariate statistical methods that take into account the underlying dependence structure when comparing experimental conditions. Specifically, we are developing methods for testing multivariate stochastic order among ordered experimental conditions. The new methods are not only more powerful than some of the existing methods, but they also provide biologically interpretable results. Increasingly researchers are using quantitative high throuput screening assays to screen thousands of chemicals for toxicity. In this research project we are developing statistical methods for analyzing such high dimensional data. Statistical methodologies are also being developed in this research project for analyzing data obtained from cell-cycle and circadian clock experiments as well as the human microbiome data. These new methods make use of the underlyng geometry in the data.